Fast approximations of spectral lineshapes to enable optimization of a filtered Rayleigh scattering experiment

Abstract

Measuring the properties of scattered light is central to many laser-based gas diagnostic techniques, such as filtered Rayleigh scattering (FRS). Alongside the measurements, a model of the scattered light’s spectral lineshape is often used to extract quantitative information about the flow field like pressure, temperature, and velocity. In particular, the Tenti S6 or S7 model are frequently used to model the lineshape of Rayleigh–Brillouin (RB) scattered light. While accurate, it is well attested in the literature that these models can be computationally expensive when evaluated many times, for example, as part of iterative estimation or optimization routines. To overcome this, approximations of these spectral lineshape models can be used instead. In this paper, we develop a method called support vector spectrum approximation (SVSA). This method uses support vector regression and singular value decomposition to create efficient, accurate, and well-conditioned approximations of any existing spectral lineshape model. The SVSA framework improves upon existing approximation methods by allowing quick calculation of spectral lineshapes for arbitrary flow regimes with any number of input parameters over a wide range of values. We demonstrate the efficacy of SVSA in approximating coherent and spontaneous RB scattering spectra. In application, we use SVSA to optimize the design of a filtered Rayleigh scattering experiment of a complex shock-dominated flow. SVSA allows us to comprehensively minimize expected measurement uncertainty of number density and temperature for this experiment. It does this by enabling a high-resolution design of experiments that is otherwise intractable.